Mat leave / Centrelink help

Hi ladies, FTM here. Baby is due September and originally I told work I’ll leave 6 weeks before, but things are getting quite nasty as they hate I’m pregnant and it actually put me in hospital stress induced Braxton hicks 30 mins apart and looked like early labour. Turns out it is legit just severe stress. I’ve looked at centrelink and it seems to suggest you can leave 6 weeks early and get mat leave OR if you need to leave earlier, you can but with a doctors note to confirm it’s medically needed and can’t be more than 12 weeks before baby is due. Centrelink is a horrible world to navigate so I just wanted to see am I understanding their policies correct? I’ve suffered my job this long so I can stick it out longer, especially when 20k or so is on the line. Thanks so much!